Column: Part 2 Courtesy of Dr. Latifee s IMI research group, Text books and others

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1 Column: Part 2 Courtesy of Dr. Latifee s IMI research group, Text books and others Design for Axial Load: With negligible moment and considerable amount of concentric axial load, failure occurs when the concrete strain reaches ultimate stain of However, considering the design safety factors, the ultimate strain may be restricted to The stress and strain distribution in pure axially loaded column is shown in the figure (a) (b) Figure: (a) stress distribution in axially loaded column, (b) maximum strain at compression failure Ideally, if a column is subjected the pure axial load, concrete and reinforcing steel undergo same amount of shortening. Concrete reaches its maximum strength at 0.85fʹc (ksi or MPa) first. Then, concrete continues to yield until steel reaches its yield strength, f y (ksi or MPa). The nominal strength of a reinforced concrete column is the sum of contribution from concrete [0.85fʹc (A g - A st ), where fʹc is compressive strength of concreter, A g is gross area of column; A st is areas of reinforcing steel] and reinforcing longitudinal steel [A st f y ]. Thus the nominal strength of a column is, P n = 0.85fʹc (A g -A st )+A st f y P n = 0.85fʹcA g +A st (f y -0.85fʹc) P n = A g [0.85fʹc+ρ g (f y fʹc)] For design purpose, ACI specify column strength as follows: For tied column, φp n(max) = 0.80φA g [0.85fʹc+ρ g (f y fʹc)] (kips) ACI Eq. (10-2) For spiral column, φp n(max) = 0.85φA g [0.85fʹc+ρ g (f y fʹc)] (kips) ACI Eq. (10-1) Where A g = gross area of column, in 2 A st = total area of longitudinal reinforcement, in 2 ρ g = A st /A g, φ= strength reduction factor The factors 0.85φ and 0.8φ are considering the effect of confinement of column ties, strength reduction due to failure mode and accidental eccentricities. The strength reduction factor φ is taken as 0.75 for columns with spiral reinforcement and 0.65 for with tie reinforcement. Preliminary column sizing: To minimize the design time, effective initial selection of column size is very important. Generally, a preliminary column size should be determined using a low 28

2 percentage of reinforcement to facilitate the possibility to provide required additional reinforcement in the final design without changing the column size. 1% to 2% reinforcement ratios usually results in the most economical design. Though the maximum amount of steel could be 8% (ACI 10.9), most columns are designed with ratios below 4 % of the gross cross-sectional area of the column considering the economy and to avoid congestion of the reinforcement. Concrete is more cost effective than reinforcement for carrying compressive axial load; thus, it is more economical to use larger column sizes with lesser amounts of reinforcement. Also, columns with a smaller number of larger bars are usually more economical than columns with a larger number of smaller bars. The design charts presented in figures below are based on ACI Eq. (10-2) can be used predict the size required for non-slender tied square column for design factored load, P u. For different combination of concrete strength and steel grade with reinforcement ratios between 1% and 8% are considered. These can be used for column sizes from 10 in. to 24 in. with negligible eccentricity (no more than 0.1 h, here h is the size of column). The figures below can also be used to determine the required column area for corresponding axial load. To fast-track the selection procedure with minimum reinforcement ratio (1%), table 1 can be used directly. Figure: Design chart for non-slender square tied column (fʹc= 4 ksi, f y = 60 ksi) 29

3 Figure: Design chart for non-slender square tied column (fʹc= 4 ksi, f y = 72.5 ksi) Table 1: Design table for non-slender tied column with minimum steel ration (1%) Steel grade, f y (ksi) Concrete strength, fʹc (ksi) 12 Minimum steel ratio, ρ g(min) Required column area, A g (in 2 ) P u / P u / P u / P u / P u / % P u / P u / P u / P u / P u / P u / P u / P u / P u / P u / P u / % P u / P u / P u / P u / P u / P u /

4 Figure: Composite Column Behavior of Tied and Spirally-Reinforced Columns Axial loading tests have proven that tied and spirally reinforced columns having the same cross sectional areas of concrete and steel reinforcement behave in the same manner up to the ultimate load, as shown in Figure below. At that load tied columns fail suddenly due to excessive cracking in the concrete section followed by buckling of the longitudinal reinforcement between ties within the failure region. For spirally reinforced columns, once the ultimate load is reached, the concrete shell covering the spiral starts to peel off. Only then, the spiral comes to action by providing a confining force to the concrete core, thus enabling the column to sustain large deformations before final collapse occurs. (a) (b) Figure: Failure of columns; (a) behavior of tied and spirally reinforced columns; (b) failure of columns Factored Loads Load factors for dead, live, wind or earthquake live loads combinations are shown in the Table below. 31

5 Table: Load factors for dead, live, wind or earthquake live loads combinations Write Short note on Ties in the column with detail figures Ties in the column When tied columns are used, the ties shall not be less than #3, provided that the longitudinal bars are #10 or smaller. The minimum size is #4 for longitudinal bars larger than #10 and for bundled bars. Deformed wire or welded wire fabric with an equivalent area may also be used (ACI ). In SI units, ties should not be less than #10 for longitudinal bars #32 or smaller and #13 for larger longitudinal bars. Spacing of Tie bar: ACI Code specifies that vertical spacing of ties is not to exceed the smallest of: 16 times longitudinal bar diameter. 48 times tie diameter. Least cross sectional dimension. ACI Code specifies that ties are arranged in such a way that every corner and alternate longitudinal bar is to have lateral support provided by the corner of a tie with an included angle of not more than 135 degrees. Besides, no longitudinal bar is to be farther than 15 cm clear on each side along the tie from such a laterally supported bar. When longitudinal bars are located around the perimeter of a circle, circular ties are used. 32

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7 Figure: Tie arrangements 34

8 Example 1: 35

9 Example 2 36

10 Axial Load and Bending Columns will bend under the action of moments, and those moments will tend to produce compression on one side of the columns and tension on the other. Depending on the relative magnitudes of the moments and axial loads, there are several ways in which the sections might fail. The column is assumed to reach its ultimate capacity when the compressive concrete strain reaches

11 Example 3 Required area of steel for a rectangular tied column with bars on four faces (slenderness ratio found to be below critical value) For a rectangular tied column with bars equally distributed along four faces, find area of steel. 38

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15 Figure: Column cross sections for normalized interaction curves Example 4: 42

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